发表机构
TUM School of Computation, Information and Technology; Munich Center for Machine Learning (MCML)（慕尼黑工业大学计算、信息和技术学院; 慕尼黑机器学习中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对各向异性CBO仅在可分目标函数上表现良好、微小坐标旋转即会严重降效的问题，提出重参数化方案估计线性变换坐标并应用CBO，提升了高维优化性能。
AI 中文摘要
基于共识的优化（Consensus-based optimization, CBO）是一种高效的全局优化元启发式算法，具有良好的数学性质，即使在非凸场景下也能保证全局收敛性。但与大多数基于粒子的优化器类似，它在实际应用中受维度灾难影响严重。已有多种策略被提出以将CBO应用于高维优化问题，其中最突出的是所谓的各向异性噪声模型。然而，Bonandin等人的最新研究指出，该方法主要在可分目标函数上表现良好，即使微小的坐标旋转也会严重降低其性能。受此观察启发，本研究探讨目标函数仅在经过线性变换的坐标系中可分的情况。为利用各向异性CBO的高效性，我们提出一种重参数化方案，该方案可证明地估计此类坐标变换，随后在新变量上应用CBO。此外，我们展示了该方案可被解释为CBO中的噪声自适应。数值示例凸显了该方法的有效性，在具有挑战性的基准目标上实现了显著的性能提升。
英文摘要
Consensus-based optimization (CBO) is an efficient metaheuristic for global optimisation with attractive mathematical properties, allowing global convergence results even in non-convex settings. In practice it suffers greatly from the curse of dimensionality, as do most particle-based optimisers. Different strategies have been proposed to apply CBO even for high-dimensional optimisation problems, the most prominent being the so-called anisotropic noise model. However, a recent work by Bonandin et al. highlighted that this method performs well primarily on separable objective functions, and even small coordinate rotations severely degrade the performance. Motivated by this observation, in this work we study the case where the objective function is separable only in a linearly transformed coordinate system. To leverage the efficiency of anisotropic CBO we propose a reparametrisation scheme, which provably estimates such a coordinate transformation and then applies CBO in the new variables. Furthermore, we show how our scheme can be interpreted as noise adaptation in CBO. Numerical examples highlight the efficacy of the method, demonstrating significant performance improvements on challenging benchmark objectives.
